$95$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $85$ less than $3$ times the number of away team fans. How many home team and away team fans attended the game?
Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 95}$ ${x = 3y-85}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${3y-85}$ for $x$ in the first equation. ${(3y-85)}{+ y = 95}$ Simplify and solve for $y$ $ 3y-85 + y = 95 $ $ 4y-85 = 95 $ $ 4y = 180 $ $ y = \dfrac{180}{4} $ ${y = 45}$ Now that you know ${y = 45}$ , plug it back into ${x = 3y-85}$ to find $x$ ${x = 3}{(45)}{ - 85}$ $x = 135 - 85$ ${x = 50}$ You can also plug ${y = 45}$ into ${x+y = 95}$ and get the same answer for $x$ ${x + }{(45)}{= 95}$ ${x = 50}$ There were $50$ home team fans and $45$ away team fans.